Risk Measures: Robustness, Elicitability, and Backtesting

Abstract

Risk measures are used not only for financial institutions rsquo internal risk management but also for external regulation (e.g., in the Basel Accord for calculating the regulatory capital requirements for financial institutions). Though fundamental in risk management, how to select a good risk measure is a controversial issue. We review the literature on risk measures, particularly on issues such as subadditivity, robustness, elicitability, and backtesting. We also aim to clarify some misconceptions and confusions in the literature. In particular, we argue that, despite lacking some mathematical convenience, the median shortfall mdash that is, the median of the tail loss distribution mdash is a better option than the expected shortfall for setting the Basel Accords capital requirements due to statistical and economic considerations such as capturing tail risk, robustness, elicitability, backtesting, and surplus invariance.